The state complexity of trellis diagrams for a class of generalized concatenated codes

Abstract

We discuss the state complexity of trellis diagrams for a class of generalized concatenated codes. The maximum number of states in the 64-section minimal trellis diagram for all the extended BCH codes of length 64 which are permuted by using the bases shown previously by Kasami et al. (1993), are the same as those obtained by Vardy and Be'ery (1993), where bit orderings were found by using DS structure and computer search. We construct several decomposable codes for which a multistage decoding up to the minimum distance can be employed. The dimensions of constructed codes are 47, 43 and 24 for length 63, and 52 and 32 for length 72. We also construct codes of length 64 as shortened codes of the codes with length 72.<>